Renewable energy sources appear as the best solution for worldwide power shortage and environmental pollution. In particular, the focus is on solar as it offers inexhaustible, clean and free energy which is abundantly available at various parts of the world. The demand of photovoltaic (PV) is also increasing as solar energy is deployed for residential and industrial purposes (Rajabi et al., 2022). In this regard, the optimization of solar power generation is important as it reduces system operational cost and number of PV panels and improves system efficiency. This is achieved through maximum power point tracking (MPPT) algorithm that ensures maximum output PV power under varying conditions (Millah et al., 2021).

With an increased rate of utilization of PV, researchers have focused on developing new MPPT techniques to extract maximum power from the PV system. Different MPPT methodologies have been introduced which can be broadly categorized as metaheuristic optimization, control law based MPPT, and machine learning based MPPT techniques. Machine learning based radial basis function neural network (RBNN) has been proposed in (Khan et al., 2021), which has a fast convergence but cannot accommodate continuous chattering as neural network needs continuous training. Genetic algorithm (GA) based MPPT with an artificial neural network (ANN) has also been proposed for MPPT which demonstrated reasonable tracking speed and DC power output (Ali et al., 2018). However, this technique is difficult to implement due to complexity arising from increased system dynamics. ANN based MPPT approach for PV electric vehicle is studied in (Bhatia et al., 2020) where open circuit voltage and temperature of solar cell were used as input variables while MPP voltage was the output variable. In addition to ANN and GA, fuzzy logic controller is also used for PV systems which is relatively easy to design since knowledge of an accurate MPPT model is not required (Dehghani et al., 2021). However, continuous training and high-error susceptibility are major issues. Conventional perturb and observe (P&O) strategy is also used for MPPT control due to its fast convergence and simplicity (Ahmed and Salam, 2018). In general, machine learning MPPT techniques achieve high efficiency, fast convergence and reduced oscillations but are costly and computationally extensive. Moreover, the systems cannot capture partial shading condition (PSC) under global MPP.

To deal with the issue of PSC, bio-inspired metaheuristic optimization based techniques are employed. Shuffled frog algorithm has been proposed in (Aldosary et al., 2021) to address this anomaly and improve MPPT controller for battery integrated PV system but the technique is inefficient under rapidly changing atmospheric conditions. Hybrid whale optimization algorithm has been discussed in some literature which has a high efficiency but it requires accurate data set and works for finite time limits (Tao et al., 2021). Although the metaheuristic techniques have various advantages, none of these optimizers address optimization problem with different constraints (Shams et al., 2021). In fact, existing research has examined the optimizers for a single or few patterns of irradiance without comprehensive statistical analysis. For instance, the gray wolf optimizer in (Jegha et al., 2020) has shown tracking accuracy under a certain set of irradiance while the impact of temperature is neglected. Dragonfly and adaptive cuckoo search optimization are presented in (Mirza et al., 2019) where variations are proposed to reference voltage for rapid global convergence among multiple PV systems. The performance of all metaheuristic optimization-based MPPT strategies is dependent on population size, number of iterations, convergence speed and effectiveness of the information sharing method.

Closed-loop MPPT control strategies aim to overcome the shortcoming of computational complexity offered by metaheuristic optimization techniques. Non-linear closed-loop schemes have been widely used in PV systems. A robust non-linear backstepping controller (BSC) for MPPT tracking is analyzed in (Ali et al., 2020), which relies on reference power generation through neuro-fuzzy approach. This system is designed for a single irradiance value and requires re-training as irradiance changes. A similar technique is discussed in (Awais et al., 2020) where the non-linear controller is linearized for a certain field data. However, this scheme is infeasible for practical PV systems which experience constantly changing environmental conditions. Sliding mode control (SMC) is one of the widely employed non-linear closed-loop method which offers various advantages such as disturbance rejection, parameter variation insensitivity and decoupled design (Aguilar et al., 2019). SMC can overcome the issue of uncertainty limits to an extent. In the presence of large uncertainties, controller gain has to be increased which enhances chattering effect (Skik and Abbou, 2016). Backstepping terminal sliding mode (BTSM) controller is discussed in (Behih and Attoui, 2021) to extract maximum power of PV system. However, it can only track MPPT curve and fails to provide controlled compensation to variations in irradiance and temperature. Non-linear control law based double integral sliding mode controller is studied in (Pradhan and Subudhi, 2016) which reduces the steady state error of MPPT through an integral component. This error reduction is at the expense of distorted transient response with increased chattering. Second order sliding mode MPPT controller has also been studied in some literature but it generates inaccurate reference current and hence, an inaccurate optimal power extraction (Peng et al., 2019). A comparison of these control techniques is highlighted in Table 1.

This paper presents a robust non-linear backstepping based real twisting sliding mode control for MPP tracking in PV battery systems. In the proposed scheme, the regression plane is generated by the predicted maximum power point voltage using linear interpolation which gives high accuracy. Contrary to other autonomous schemes which deploy droop control for DC bus voltage regulation, in this paper, a direct sliding mode control is proposed which helps regulate voltage under varying irradiance, temperature and loads. The system topology consisting of PV, battery, boost, and buck-boost converter is simulated and analyzed in MATLAB where it is observed that the proposed scheme has a good tracking with reduced overshoot, chattering and settling time. The optimal performance of the proposed control is also highlighted in comparison with other well-established control strategies.

The rest of the paper is organized as follows: Section 2 discusses the system topology and converter control. Section 3 presents back stepping based real twisting sliding mode control while the power management and parameter design are analyzed in Section 4. Simulation results and discussion are given in Section 5, followed by conclusion in Section 6.

The system topology consists of PV module and battery linked to DC bus via buck-boost converters. This is shown in Figure 1. The battery buck-boost converter is bidirectional and can operate in either buck or boost mode depending on the current drawn from the source. It consists of two loops: an outer voltage control loop with PI controller and an inner current control using SMC. This helps regulate the DC bus voltage. Linear interpolation-based regression plane is employed to generate the reference voltage signal for PV. The modeling of PV and buck-boost converters along with the control schemes are discussed as follows.

The first step in controller design involves calculations of error between actual and desired PV output voltage. Thus, ɛ ₁ defined as the difference between actual and expected output voltage of a solar PV system: ε 1 = V p v − α 1 r e f (14) where α _1ref is the reference PV voltage. Combining (11) and (14), we have: ε ̇ 1 = I p v C i − μ x 2 C i − α 1 r e f . (15) To reduce error signal to zero, we need to treat α ₂ as a virtual control input which should satisfy Lyapunov stability theory. Thus, the time derivative of Lyapunov term V 1 = 1 / 2 ε 1 2 along with (15) leads to: d V 1 d t = ε 1 I p v C i − μ α 2 C i − α 1 r e f . (16) α 2 = I p v C i + K 1 ε 1 − α 1 r e f . C i μ (17) The constant K ₁ in (17) must be a positive constant for any specific x ₂. Hence, (16) can be rewritten as: d V 1 d t = − K 1 ε 1 2 (18) The stabilization function acts as a reference for x ₂ as: α 2 r e f ′ = I p v C i + K 1 ε 1 − α 1 r e f . C i μ (19) The second state needs a new reference for further tracking. In this regard, α 2 r e f ′ is chosen as the new reference and the tracking error can be defined as: ε 2 = x 2 − α 2 r e f ′ (20) Solving (16) and (19) leads to: d V 1 d t = ε 1 I p v C i − μ α 2 r e f ′ C i − α 1 r e f . − μ ε 2 C i (21) Substituting (19) in (21), we have: d V 1 d t = − K 1 ε 1 2 − μ ε 1 ε 2 C i (22) Differentiating (20) with respect to time leads to: ε ̇ 2 = x ̇ 2 − α 2 r e f ′ ̇ (23) Therefore, the time derivative of α 2 r e f ′ can also be calculated as: α 2 r e f ′ ̇ = 1 μ 2 μ X ̇ − μ ̇ X (24) where X = I p v − C i α 1 r e f . + K 1 C i ε 1 . By multiplying and dividing by μ, (24) can be expressed as: α 2 r e f ′ ̇ = 1 μ I p v ̇ − C i α 1 r e f ¨ − K 1 2 C i ε 1 − K 1 ε 2 − μ ̇ μ α 2 r e f (25) To ensure convergence of errors ɛ ₁ and ɛ ₂ to zero, a composite Lyapunov function V _c is defined as: V c = V 1 + 1 2 ε 2 2 (26) The time derivative of V _c is given as: d V c d t = − K 1 ε 1 2 + ε 2 ε ̇ 2 − μ ε 1 C i (27) For V _c to be negative, let: ε ̇ 2 − μ ε 1 C i = − K 2 ε 2 (28) which can be expanded as: − K 2 ε 2 = − μ x 3 L + μ x 1 + x 3 L + K 1 ε 2 + μ ̇ μ α 2 r e f − μ ε 1 C i − 1 μ I p v ̇ − C i α 1 r e f ¨ − K 1 2 C i ε i (29) Thus, the backstepping based equivalent control law becomes: μ e q ̇ = 1 α 2 r e f ε 2 − K 1 − K 2 μ − ε 1 K 1 2 C i − μ 2 C i + μ x 3 L + 1 α 2 r e f I p v ̇ − C i α 1 r e f ¨ − μ 2 x 1 + x 3 L (30) This control law modifies (27) to an alternate form as: d V c d t = − K 1 ε 1 2 − K 2 ε 2 2 (31) where 0 < μ < 1 and α _2ref ≠ 0.

From (31), it can be observed that the derivative of Lyapunov function is negative definite. Therefore, the design of proposed controller is globally asymptotically stable.

The Real twisting sliding mode-based discontinuous control Law is designed as (Bjaoui et al., 2019): μ s w ̇ = − K 3 S i g n ε 1 − K 4 S i g n ε ̇ 1 − K 5 ε 1 (32) The modified control law is used for mitigating chattering effect in higher order non-linear system. The proposed backstepping based real twisting sliding mode control law, is given as: μ ε ̇ = μ e q ̇ + μ s w ̇ = K 3 S i g n ε 1 + K 4 S i g n ε ̇ 1 + K 5 ε 1 + 1 α 2 r e f ε 2 − K 1 − K 2 μ − ε 1 K 1 2 C i − μ 2 C i + μ x 3 L + 1 α 2 r e f I p v ̇ − C i α 1 r e f ¨ − μ 2 x 1 + x 3 L (33) The proposed algorithm in this paper uses a continuous control function that drives the sliding variable and its derivative to zero in finite time. By twisting the state trajectories around the origin, convergence independent of constrained perturbations is achieved that retains good performance despite variations and uncertainties. The flow chart of algorithm is shown in Figure 5.

Bidirectional buck-boost converters can operate in buck mode or boost mode depending on the power flow direction. Two control modes need to be deployed to operate the converter in desired mode of operation and based on the battery current direction, required mode should be triggered. It is worth mentioning that the objective of both modes is to regulate DC bus voltage.

In the battery control, outer voltage loop produces the current reference for inner current control. Assuming negligible losses in the system, the dc current can be expressed as: I d c = 1 V d c I p v V p v + I BESS V BESS − I load V d c (34) Battery current I _BESS is used to regulate I _dc to its reference I _dc,ref . Hence, (34) can be written as: I BESS,ref = 1 V BESS I d c , r e f V d c + I load V d c − I p v V p v (35) The sliding surface for the inner current loop of battery controller is chosen as: δ = I BESS,ref − I BESS (36) The battery current and DC bus voltages reach their reference values in a finite time. Correspondingly, SMC controls PWM signal which is used in buck and boost modes.

To analyze the proposed control scheme, the system in Figure 1 is built in Simulink. The DC bus voltage is 200 V while the PV system has maximum power rating of 25 kW with solar irradiance 1000 W/m² and operating temperature of 298K/25°C. The system parameters are obtained from (45–50) and are highlighted in Table 2 where (K ₁, K ₂, K ₃, K ₄, K ₅) are gains of BRTA while (K ₆, K ₇) are gains of SMC, respectively.

The PV panel regression plane is shown in Figure 6. It provides a reference voltage for the non-linear controller to achieve MPP under fluctuating temperature and irradiance conditions. The PV module characteristic curve is used to build the V _mpp matrix for various temperature and irradiance levels. The regression plane is obtained via linear interpolation, which gives the reference voltage, α _1ref , to the controller. To achieve MPP, the backstepping based real twisting controller follows reference voltage α _1ref as: α 1 r e f = 579.81 − 1.9899 T − 0.12146 I r r (51)

At initial steady state, PV panel is producing 25 kW and load power consumption is 10 kW. The battery is in charging mode with 15 kW. The control law in (33) determines the desired PV voltage while BRTA extracts maximum power point by tracking the desired PV voltage obtained by linear regression method. System performance is studied through the following changes.

1) The irradiance of PV panel varies from 1000 W/m² to 850 W/m² at t = 1 s.

This paper presents a robust non-linear backstepping based real twisting sliding mode control for MPP tracking in PV battery systems. In the proposed scheme, the regression plane is generated by the predicted maximum power point voltage using linear interpolation which gives high accuracy. Contrary to other autonomous schemes which deploy droop control for DC bus voltage regulation, in this paper, a direct sliding mode control is proposed which helps regulate voltage under varying irradiance, temperature and loads. The system topology consisting of PV, battery, boost, and buck-boost converter is simulated and analyzed in MATLAB where it is observed that the proposed scheme has a good tracking with reduced overshoot, chattering and settling time. The optimal performance of the proposed control is also highlighted in comparison with other well-established control strategies, making it an ideal candidate for future PV-battery systems.

For future work, the proposed scheme can be integrated with machine learning techniques to further improve the system performance. The system can be expanded to include AC and DC sources to analyze dynamics. Moreover, the hardware prototype should be developed to ensure coherence between simulated and measured values.